Dusty’s exchanges
with Mrs Dogood were a stock feature of America’s Puck magazine:

Dusty
Rhodes. – Lady, did I understand you to say "beef"?

Mrs.
Dogood. – I said "biff".

Puck (1891), 14 October
p. 115

Increasingly, Dusty’s
exploits came to be illustrated, by individual sketches or cartoons rather than
in a strip (see, for example, Puck on
10 October 1894). Puck published a
‘library’ of comic books too. No 107, “Knights of the Road”, came out in mid
1896, advertised as “Puck’s Best Things About Dusty Rhodes & Co.”

But to find a regular source of Dusty Rhodes
comic strips on this side of the Atlantic, we need to look at Chips (or in full Illustrated Chips), a comic magazine published by Harmsworth from
1890. We know from the list of magazines stocked by the Dublin newsagent Tallon that Chips was readily available to a Dublin
audience in 1898.

Chips is better known for
the regular comic strip by Tom Browne featuring Weary Willie and Tired Tim, who
ambled their way through the comic from 1896. Dusty Rhodes in fact makes his
appearance slightly earlier, in 1894. A comic strip for 7 July is entitled
“Dusty Rhodes Gets a Regular Dyeing”, in which Dusty clambers into a dog kennel
which has been booby-trapped with paint by two conspiratorial boys. By August
1898 we see the “guy in the mackintosh” that Joyce refers to, in a strip
entitled “Rather Tall, But Strictly Untrue!”:

Dusty Rhodes doesn’t compete with the likes
of Weary Willie and Tired Tim. His own sidekicks are often the less renowned
Weary Walker and Tatterden Torne. But by the first decade of the twentieth
century they were well enough known to make occasional illustrated appearances
in the Weekly Irish Times.